Show us a scripture that says what you say: that Acts is a transitional book. It is a part of Scripture, and therefore is usable for Doctrine according to Paul.
Now, since you asked:
First, let's ask the question: when would Philip baptize people in water?
Acts 8:
36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
38 And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.
I think we can say that Philip would not baptize people in water UNTIL he was SURE they believed in Jesus.
Then Philip went down to the city of Samaria, and preached Christ unto them.
6 And the people with one accord gave heed unto those things which Philip spake, hearing and seeing the miracles which he did.
[if they are giving heed, are they believing? I think that goes without saying.]
7 For unclean spirits, crying with loud voice, came out of many that were possessed with them: and many taken with palsies, and that were lame, were healed.
8 And there was great joy in that city. [why great joy? I think this hints that they all were born again.]
12 But when they believed Philip preaching the things concerning the kingdom of God, and the name of Jesus Christ, they were baptized, both men and women. [We already established that Philip would not baptize unless he was SURE they were truely believers.]
14 Now when the apostles which were at Jerusalem heard that Samaria had received the word of God, they sent unto them Peter and John: [Now we get a look at what those in Jerusalem were THINKING: why send more people? Was Philip not able to pray for the baptism of the Holy Spirit? Aparently those in Jerusalem did not think so. Philip had proven he could get people born again, but Peter and John apparently had proven they could get people filled with the Holy Spirit.
15 Who, when they were come down, prayed for them, that they might receive the Holy Ghost: [here the actual prayer took place.]
16 (For as yet he was fallen upon none of them: only they were baptized in the name of the Lord Jesus.) [Notice this is not talking about the Holy Spirit within as in salvation: they were already saved and baptized in water. This is talking about the Holy Spirit UPON as in the anointing for power.]
17 Then laid they their hands on them, and they received the Holy Ghost. [Notice that nowhere in scripture is the laying on of hands required for salvation. Only hearing the word and believing is required for salvation. But for the baptism, it was usual to lay on hands as they prayed. ]
We find this same sequence in Acts 19.
Did you not read? Acts 11:
15 And as I began to speak, the Holy Ghost fell on them, as on us at the beginning.
16 Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost.
17 Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?
God was proving that there was NO DIFFERENCE between Jew or Gentile: both could receive salvation by faith and then receive the Holy Spirit.
Why worry about "transitions?" Just read the text and believe it! Way back in Joel God promised the day would come when the Holy Spirit would be poured out on all flesh - and Peter told us that prophecy began to be fulfilled at Pentecost, and is still ongoing.
The truth is, we will be judged by Paul's gospel. He has written in out in 1 Cor. 15: the death, burial and resurrection of the Lord Jesus Christ is the basis for Paul's gospel. But when we read 1 Cor, 12 and 14, we see that Pentecost and the baptism of the Holy Spirit was also very much a part of His gospel.
I wonder: could YOU as a fellow believer what Paul asked those in Ephesus: "have you received the Holy Spirit since you believed?"
If not, they your believing is not what Paul believed.